EXPERIMENT 3 Fresnel Reflection

1. Reﬂectivity of polarized light

The reflection of a polarized beam of light from a dielectric material such as air/glass was described by Augustin Jean Fresnel in 1823. While his derivation was based on an elastic theory of light waves, the same results are found with electromagnetic theory. The ratio of the reflected intensity to the incident intensity is called the reflectivity of the surface. It depends on the polarization of the incident light wave. Let be the angle of incidence and be the angle of transmission. Snell’s law relates these according to the refractive index in each media and :

( ) ( ) (1)

The reﬂectivity for light polarized parallel to the plane of incidence (known as p-polarized light) is

( ) (2) ( ) but for light polarized perpendicular to the plane of incidence (known as s-polarized light) it is

( ) (3) ( )

Notice that for p-polarized light the denominator of the right hand side will be inﬁnite when the sum ( ) . The angle of

1 incidence when this happens is called Brewster’s angle, . For light polarized in the plane of incidence, no energy is reﬂected at Brewster’s angle, i.e. .

2. Making the measurements

Getting started: A He-Ne laser (632.8 nm) beam is reﬂected from the front face of a prism on a rotating table. You can read the angle of rotation of the table from the precision index and vernier. It is very important to locate the center of the prism over the axis of rotation. Do this as best you can by eye. As the prism is rotated so that the light grazes its surface the laser will miss the prism unless everything is aligned well.

Find the reading for normally incident light: Rotate the table so that the laser beam returns back to the face of the laser, centered exactly on the laser aperture. You may need to level the laser beam by adjusting the screws on its support. Read the angular scale on the table carefully. This is the reference for all future measurements of angle since rotations from this angle change the angle of incidence from by exactly that amount. Figure 2.1 illustrates a horizontal view of the experiment.

Measure the light intensity at diﬀerent angles: Turn on the voltmeter. Its reading measures the intensity of the light in the beam from the output voltage of a selenium photovoltaic cell. Set the electric vector of the polarizer horizontal: the indices on the polarizing ﬁlter mark the direction of the electric vector of the transmitted light. The light leaving the horizontal polarizer is now polarized in the plane of incidence. Take a direct

2 reading of the laser after the beam passes through the polarizer. When you make this measurement, insert an attenuation filter to reduce the intensity of the direct laser beam so that it is comparable to the reflected light you will be measuring. This minimizes the importance of nonlinear response from the detector for very intense sources. Remove the neutral density filter, and follow with a series of ten or more readings of the reflected light intensity for different angles of the prism table. You cannot measure normal incidence, since the reflected light just goes back to the laser in that case. You also cannot measure grazing incidence, but from about to the reflected beam is accessible.

Figure 2.1: Light from the laser at the right is directed to the center of a face of a prism on a rotating table in this horizontal view of the Fresnel coeﬃcient experiment. The

laser is leveled so that the beam returns exactly back on itself. The prism is adjusted so that its face is exactly over the axis of rotation of the mounting.

Correct, tabulate, and graph the results: Subtract the table angle for normal incidence from the other angle measurements. The table reading corrected in this way is just the angle of incidence. Tabulate these measurements and plot the measured intensity divided by the incident signal measurement versus this angle. Remember that you had an attenuation ﬁlter in when you measured the laser directly, so you must multiply those measurements by the ﬁlter factor.

Repeat it again with perpendicular polarization:

Rotate the polarizer to make the light polarized perpendicular to the plane of incidence, and take another set of about 10 measurements. Tabulate, correct, and plot these measurements on a separate graph.

3. Analysis of your results

Determine Brewster’s angle The intensity of the light polarized parallel to the plane of incidence should go to zero at Brewster’s angle. Determine Brewster’s angle from the graph as accurately as you can. According to the Fresnel equations, Brewster’s angle is related to n by

( ) (2)

Consider that in our experiment the incident medium is air with

. Determine the index of refraction of the glass from your

4 experimental data.

Compare to the theoretical equations: Calculate a series of values for the Fresnel equations using the index of refraction determined from Brewster’s angle. Create files on the PC with your experimental and calculated values. Plot the calculated reflectivities on the same graphs with the experimental data. The curves should be very similar. If they are on really different scales, you may have made an error normalizing the signal to the direct laser light. If so, check how you corrected for the attenuation filter. Include screen dumps of the graphs with your lab report.

Identify the source of errors: There are sure to be discrepancies remaining between your measurements and the values of the Fresnel reﬂectivities. Identify the source of any major differences.

And think about: Why do we use a prism in this experiment, rather than a glass plate? Why doesn’t the reﬂected beam go away entirely at Brewster’s angle when the polarization is parallel to the plane of incidence?